Airp said:Homework Statement
F(x)= x-12x1/3 Find the X-intercept
Homework Equations
X-intercept means y=0
The Attempt at a Solution
My math teacher gave plus or minus 24sqrt3 as an answer, but I have no idea how he got that! He also got 0, but I do understand that one... I just don't know how to get the 24sqrt3 Could someone help me, please?
Thank you so much! This community really is awesome!RUber said:The u-substitution is all you need. However, the answer you get is for u. x = u^3. So you will cube your answer.
There should be no reason to cube 12. That would be assuming that
##F(x)^3=(x-12x^{1/3})^3 = x^3 - 12^3 x## but that is not how powers of polynomials work.
Edit:
However, in this case, since you are assuming that F(x) = 0 (x- intercept), you will get the right solution since:
##0=x-12x^{1/3}##
##x=12x^{1/3}##
##x^3=12^3x##
##0=x^3-12^3x##
There are many ways to get to the answer...just be sure you know why you are doing things.
The x-intercept of a function is the point where the graph of the function crosses the x-axis. It is the value of x where the function's output, or y-value, is equal to zero.
To find the x-intercept of a function, set the function equal to zero and solve for x. This will give you the x-coordinate of the intercept point. You can also graph the function and visually determine the x-intercept by locating where the graph intersects the x-axis.
Yes, a function can have multiple x-intercepts. This occurs when the function crosses the x-axis at more than one point. In some cases, a function may not have any x-intercepts if the graph does not intersect the x-axis.
The x-intercept provides information about where the function crosses the x-axis, which can be useful for analyzing the behavior of the function. It can also be used to find the roots or solutions of the function, as the x-intercept corresponds to the input values where the output is equal to zero.
No, the x-intercept and the root of a function are the same thing. Both terms refer to the x-value where the function's output is equal to zero. However, the term "root" is often used in the context of solving equations, while "x-intercept" is used in reference to graphing a function.